Previous analyses of waves on shear currents impose the stream profile a priori
as a function of depth. In the present formulation, a stream function ip(x,y,t) is
assumed to exist and unknown a priori, for a stable, two dimensional combined
fluid flow of a stream of finite depth with a free surface wave disturbance of
finite wave length, periodic and of permanent form. We show that the retained
expression of the stream function is a quadratic in %/, the vertical coordinate. The
so-called current profile is not, at the outset, imposed on the solution. First and
second order wave undulations can be developed for this case.
1. Introduction
Most investigations of waves on shear currents deal with linear current
profiles. To model a rea